I have 2 problems here and i have done the formulas i come up with 0.285 =3 in the 1st problem and 36 in the 2nd problem. the correct answers are below with the problems can you please show the working so i can see where I am going wrong

PROBLEM 1

Hotel Reservations

A hotel near the MCG always fills up on the evening before football games. History has shown that when the hotel is fully booked, the number of last-minute cancellations has a mean of 5 and standard deviation of 3. The average room rate is $80. When the hotel is overbooked, the policy is to find a room in a nearby hotel and to pay for the room for the customer. This usually costs the hotel approximately $200 since rooms booked on such late notice are expensive. The demand probabilities and the associated cumulative probability distribution ( P ) for this situation are shown below.

1. How many rooms should the hotel overbook? 3

No. of no shows Probability Cumulative probability

0 0.05 0.05

1 0.15 0.13

2 0.10 0.23

3 0.15 0.38

4 0.20 0.58

5 0.15 0.73

6 0.11 0.84

7 0.06 0.90

8 0.05 0.95

9 0.04 0.99

10 0.01 1.00

PROBLEM 2

Product Sales

A product is priced to sell at $100 per unit, and its cost is constant at $70 per unit. Each unsold unit has a salvage value of $20. Demand is expected to range between 35 and 40 units for the period; 35 definitely can be sold and no units over 40 will be sold. The demand probabilities and the associated cumulative probability distribution ( P ) for this situation are shown below.

No. of units demanded Probability of this demand Cumulative probability

35 0.10 0.10

36 0.15 0.25

37 0.25 0.50

38 0.25 0.75

39 0.15 0.90

40 0.10 1.00

1. How many units should be ordered? 35